Quadratic Formula Calculator
Solve ax² + bx + c = 0 for real or complex roots.
Solving ax² + bx + c = 0 for x is one of the most common algebra problems — this applies the quadratic formula directly, handling both real and complex roots.
What the discriminant tells you before you even solve
The discriminant (b² − 4ac) predicts the nature of the roots before you finish solving: positive means two distinct real roots, zero means one repeated real root, and negative means two complex (non-real) roots — this calculator shows the discriminant alongside the solution.
Frequently asked questions
What does it mean if the roots are complex numbers?
It means the equation has no real-number solutions — the parabola described by the equation never crosses the x-axis, which is exactly what a negative discriminant indicates.
Can "a" be zero?
No — if a is zero, the equation isn't actually quadratic anymore (the x² term disappears), so it becomes a simple linear equation instead.